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A053977 Engel expansion of the Euler-Mascheroni constant gamma A001620 = 0.57721566... . 3

%I

%S 2,7,13,19,85,2601,9602,46268,4812284,147961485,210810243,814960948,

%T 1003849128,1016803038,12917183059,26242325020,22215291139324,

%U 30797877759859,60139200644343,121848657453426,133555928335475

%N Engel expansion of the Euler-Mascheroni constant gamma A001620 = 0.57721566... .

%C Cf. A006784 for definition of Engel expansion.

%D F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191.

%H T. D. Noe, <a href="/A053977/b053977.txt">Table of n, a(n) for n=1..300</a>

%H P. Erdős and Jeffrey Shallit, <a href="http://www.numdam.org/item?id=JTNB_1991__3_1_43_0">New bounds on the length of finite Pierce and Engel series</a>, Sem. Theor. Nombres Bordeaux (2) 3 (1991), no. 1, 43-53.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Euler-MascheroniConstant.html">Euler-Mascheroni Constant</a>

%H <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>

%t EngelExp[ A_, n_ ] := Join[ Array[ 1&, Floor[ A ] ], First@Transpose@NestList[ {Ceiling[ 1/Expand[ #[ [ 1 ] ]#[ [ 2 ] ]-1 ] ], Expand[ #[ [ 1 ] ]#[ [ 2 ] ]-1 ]}&, {Ceiling[ 1/(A-Floor[ A ]) ], A-Floor[ A ]}, n-1 ] ]

%Y Cf. A006784, A028254, A028257.

%K nonn,easy,nice

%O 1,1

%A _Jeppe Stig Nielsen_, Apr 02 2000

%E More terms and additional comments from _Mitch Harris_, Jan 15 2001

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Last modified December 4 17:26 EST 2016. Contains 278755 sequences.